TY  - BOOK
AU  - Ramis,Jean-Pierre
AU  - Sauloy,Jacques
AU  - Zhang,Changgui
TI  - Local analytic classification of q-difference equations
T2  - Asterisque
SN  - 9782856297759 (paperback)
U1  - 510=4 23
PY  - 2013///
CY  - Paris
PB  - Societe mathematique de France
KW  - Difference equations
N1  - Includes bibliographical references (pages 139-143) and indexes; 1. Introduction --
2. Some general nonsense --
3. The affine space of isoformal analytic classes --
4. The q-analogs of Birkhoff-Malgrange-Sibuya theorems --
5. Summation and asymptotic theory --
6. Geometry of the space of classes --
7. Examples of the Stokes phenomenon --
A. Classification of isograded filtered difference modules--
Bibliography--
Index of notations--
Index
N2  - We essentially achieve Birkhoff's program for q-difference equations by giving three different descriptions of the moduli space of isoformal analytic classes. This involves an extension of Birkhoff-Guenther normal forms, q-analogues of the so-called Birkhoff-Malgrange--Sibuya theorems and a new theory of summation. The results were announced in various seminars and conferences between 2004 and 2006
ER  -